On leafwise conformal diffeomorphisms

被引：0
|
作者：
Niedzialomski, Kamil [1 ]
机构：
[1] Univ Lodz, Dept Math & Comp Sci, PL-90238 Lodz, Poland
来源：
JOURNAL OF GEOMETRY AND PHYSICS | 2010年 / 60卷 / 01期
关键词：
Conformal mapping; Foliation; Riemannian manifold;
D O I：
10.1016/j.geomphys.2009.08.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For every diffeomorphism phi : M -> N between 3-dimensional Riemannian manifolds M and N, there are locally two 2-dimensional distributions D(+/-) such that phi is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of D(+/-). These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from phi(*). We investigate the integrability condition of D(+) and D(-). We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码：23 / 30
页数：8
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